Albon was quickest after the intermediate tyre runs but shunted with less than three minutes remaining while preparing for a late flying lap on slicks.
The session was not restarted, meaning Albon led the way from Valtteri Bottas and Sebastian Vettel – while world champion Hamilton failed to set a laptime.
Torrential rain hit Interlagos on Thursday evening and again on Friday morning, but conditions eased as the first 90-minute session began and by the end of FP1 drivers were able to complete a small amount of running on slick tyres.
Ferrari’s Sebastian Vettel was the first to brave a soaking wet track, using full wet tyres a couple of minutes into the session, but it would take another 20 minutes before a lap time was set.
Carlos Sainz posted a 1m22.149s that stood as the lone time for another 10 minutes, before Charles Leclerc went quickest on a 1m21.259s.
On his second run, after switching to intermediate tyres, Leclerc went four seconds faster and his 1m17.285s remained competitive even as conditions improved and others switched to intermediates.
Vettel displaced his Ferrari teammate with a 1m17.041s before Bottas set the first sub-1m7s lap, a 1m16.693s.
With 20 minutes remaining, Hamilton and both Red Bull drivers were among those still to set a lap time.
Albon then leapt from the foot of the times to P1, posting a 1m16.399s, while Verstappen waiting until just over five minutes were left before heading out for his first flying lap – on slick tyres.
The perils of the slippery surface were immediately evident, though, as Verstappen spun at Turn 2 shortly after Leclerc had run wide at the same place.
Daniil Kvyat had a harmless spin at Turn 1, but Albon was not as lucky as his colleagues.
The recently-confirmed Red Bull 2020 driver was completing his out-lap when he slid off the road approaching the penultimate corner.
Albon hit the barriers heavily with the front-right of his car taking the brunt of the impact, and the session was red-flagged and not restarted.
It meant no driver improved on slick tyres at the end, leaving Albon quickest from Bottas, Vettel, Leclerc, and Sainz.
Albon’s shunt also meant Romain Grosjean, Sergio Perez, Verstappen and Hamilton all failed to set a time.